Measure and integral with purely ordinal scales

9 years 2 months ago
Measure and integral with purely ordinal scales
We develop a purely ordinal model for aggregation functionals for lattice valued functions, comprising as special cases quantiles, the Ky Fan metric and the Sugeno integral. For modeling findings of psychological experiments like the reflection effect in decision behaviour under risk or uncertainty, we introduce reflection lattices. These are complete linear lattices endowed with an order reversing bijection like the reflection at 0 on the real interval [-1, 1]. Mathematically we investigate the lattice of non-void intervals in a complete linear lattice, then the class of monotone interval-valued functions and their inner product. 1 Motivation and survey Measuring and aggregation or integration techniques have a very long tradition. Here numbers play an important role. But how do humans perceive numbers? The numbers, say the set R of reals, support two basic structures, the algebraic structure defined by + and
Dieter Denneberg, Michel Grabisch
Added 09 Dec 2010
Updated 09 Dec 2010
Type Journal
Year 2008
Where CORR
Authors Dieter Denneberg, Michel Grabisch
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